SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries
This provides a foundational tool for researchers and practitioners in machine learning to analyze and compare deep network architectures, enhancing interpretability and generalizability.
The authors tackled the problem of exactly visualizing and characterizing deep network geometry and decision boundaries, developing SplineCam as the first provably exact method for computing these over specified data regions without approximations, applicable to various architectures like ReLU and max-pooling.
Current Deep Network (DN) visualization and interpretability methods rely heavily on data space visualizations such as scoring which dimensions of the data are responsible for their associated prediction or generating new data features or samples that best match a given DN unit or representation. In this paper, we go one step further by developing the first provably exact method for computing the geometry of a DN's mapping - including its decision boundary - over a specified region of the data space. By leveraging the theory of Continuous Piece-Wise Linear (CPWL) spline DNs, SplineCam exactly computes a DNs geometry without resorting to approximations such as sampling or architecture simplification. SplineCam applies to any DN architecture based on CPWL nonlinearities, including (leaky-)ReLU, absolute value, maxout, and max-pooling and can also be applied to regression DNs such as implicit neural representations. Beyond decision boundary visualization and characterization, SplineCam enables one to compare architectures, measure generalizability and sample from the decision boundary on or off the manifold. Project Website: bit.ly/splinecam.